Let's check our result by comparing the transfer function from the
input force to the force on the mass in both the discrete- and
continuous-time cases.

For the discrete-time case, we have

where the last simplification comes from the mass reflectance relation
. (Note that we are using the standard
traveling-wave notation for the adaptor, so that the
signs are swapped relative to element-centric notation.)

Thus, we have verified that the force transfer-function from the
driving force to the mass is identical in the discrete- and
continuous-time models, except for the bilinear transform frequency
warping in the discrete-time case.